What is the derivative of e^x(3x^2+5x-1) ?

The derivative of e^x(3x^2+5x-1) is 3e^xx^2+11e^xx+4e^x

What is the first derivative of e^x(3x^2+5x-1) ?

The first derivative of e^x(3x^2+5x-1) is 3e^xx^2+11e^xx+4e^x

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\frac{d}{d x} (e^{x} (3 x^{2} + 5 x - 1))

3 e^{x} x^{2} + 11 e^{x} x + 4 e^{x}

Solution steps

\frac{d}{d x} (e^{x} (3 x^{2} + 5 x - 1))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x}, g = 3 x^{2} + 5 x - 1

= \frac{d}{d x} (e^{x}) (3 x^{2} + 5 x - 1) + \frac{d}{d x} (3 x^{2} + 5 x - 1) e^{x}

\frac{d}{d x} (e^{x}) = e^{x}

\frac{d}{d x} (3 x^{2} + 5 x - 1) = 6 x + 5

= e^{x} (3 x^{2} + 5 x - 1) + (6 x + 5) e^{x}

Simplify

e^{x} (3 x^{2} + 5 x - 1) + (6 x + 5) e^{x} : 3 e^{x} x^{2} + 11 e^{x} x + 4 e^{x}

= 3 e^{x} x^{2} + 11 e^{x} x + 4 e^{x}

\int 1 - 2 cos (2 x) d x

\int \frac{1}{2 x ^{2} x ^{2} - 9} d x

f (x) = (5 x - 5)^{\frac{1}{4}}, at x = 2

\frac{d}{d x} (4 sin (x) - 5 cos (x) + x)

y^{- 2}

What is the derivative of e^x(3x^2+5x-1) ?
The derivative of e^x(3x^2+5x-1) is 3e^xx^2+11e^xx+4e^x
What is the first derivative of e^x(3x^2+5x-1) ?
The first derivative of e^x(3x^2+5x-1) is 3e^xx^2+11e^xx+4e^x